Vector Sum (Angle Theta and Magnitude)

[frozonecom]

Homework Statement

I made those illustrations up. :) We are asked to find the angle theta using the graphical method (Tail-to-Tip Method)
From these examples, Vector A + Vector B + Vector C = Resultant Vector

How to find angle theta of Resultant Vector?

Homework Equations

The Attempt at a Solution

So, should I measure the angle of the resultant vector from the positive x-axis or is my understanding wrong? All I can find on the net is algebraic method and I can't even understand this graphical method yet.

So, from illustration number 1, should it be somewhere close to 90 to 110 degrees?
I don't even have a clue on how to know the angle theta of illustrations 2 and 3.

I know using the algebraic method is much accurate and useful, but our teacher hasn't even taught us that yet. So please, someone help me? :)

 

[Disconnected]

Well, what were the magnitudes/directions of the initial vectors? How did you decide what direction they pointed/how long they were?

If you did indeed draw the vectors perfectly, then you can get not-super-accurate value for the resulting vector just by measuring it's length and direction.

 

[frozonecom]

Well, I didn't mind putting the values since I'd still be doing the measuring using the protractor by myself. I know how to measure the magnitude, I'm just asking how / what is the proper procedure in measuring angle theta using a protractor as described in the graphical method.

But if it helps here it is:

Illustration 1:
Vector A= Southwest, 8 cm
Vector B= East, 6 cm

Illustration 2:
Vector A= West, 4 cm
Vector B= 20 Degrees South of East , 5 cm
Vector C= 57 Degrees South of West, 8 cm

Illustration 3:
Vector A= SouthWest, 7 cm
Vector B= East, 4 cm

Hope you can help me with this. :) And sorry if it is so inaccurate, I did try my best to make it look like my drawing in my paper. :)

 

[Disconnected]

Have you done trigonometry? I am inclined to believe you have.
Surely you can find the unknown angle pretty easily?

You needn't draw the sketch perfectly, the important thing is the values with which you do the maths.

 

[rwisz]

Hi there! It's great to see that you are trying to understand the graphical method for finding the angle theta of the resultant vector.

To answer your question, yes, you are correct. In the graphical method using the Tail-to-Tip method, the angle theta of the resultant vector can be measured from the positive x-axis. In illustration 1, it would be somewhere between 90 to 110 degrees.

For illustration 2 and 3, the angle theta can also be measured from the positive x-axis. It may be a bit more difficult to estimate the angle in these cases, but you can use a protractor or ruler to get a more accurate measurement.

Keep in mind that the graphical method is not as accurate as the algebraic method, but it is still a useful tool for understanding vector addition. As you continue to learn and practice, you will become more comfortable with both methods. Keep up the good work!